A031298 Triangle T(n,k): write n in base 10, reverse order of digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 4, 0

Offset

0,3

Comments

The length of n-th row is given in A055642(n). - Reinhard Zumkeller, Jul 04 2012

According to the formula for T(n,1), columns are numbered starting with 1. One might also number columns starting with the offset 0, as to have the coefficient of 10^k in column k. - M. F. Hasler, Jul 21 2013

Links

Reinhard Zumkeller, Rows n = 0..2500 of triangle, flattened

Formula

T(n,1) = A010879(n); T(n,A055642(n)) = A000030(n). - Reinhard Zumkeller, Jul 04 2012

Mathematica

Table[Reverse[IntegerDigits[n]], {n, 0, 50}]//Flatten (* Harvey P. Dale, Mar 07 2023 *)

Prog

(Haskell)
a031298 n k = a031298_tabf !! n !! k
a031298_row n = a031298_tabf !! n
a031298_tabf = iterate succ [0] where
   succ []     = [1]
   succ (9:ds) = 0 : succ ds
   succ (d:ds) = (d + 1) : ds
-- Reinhard Zumkeller, Jul 04 2012
(PARI) T(n, k)=n\10^(k-1)%10 \\ M. F. Hasler, Jul 21 2013
(Python)
from oeis_sequences.OEISsequences import bisection, bsearch
def A031298(n):
    if n < 10: return n
    def g(x): return x+(m:=len(str(x)))*(x+1)-(10**m-10)//9
    def f(x): return n+1+bsearch(g, x)
    return int((s:=str(a:=bisection(f, n+1, n+1)-n))[(k:=len(s))*(a+1)-n-(10**k-1)//9]) # Chai Wah Wu, Mar 04 2026

Crossrefs

Cf. A030308, A030341, A030386, A031235, A030567, A031007, A031045, A031087 for the base-2 to base-9 analogs.

Cf. A004086 (n with digits reversed).

Sequence in context: A252648 A054054 A115353 * A004428 A004429 A338379

Adjacent sequences: A031295 A031296 A031297 * A031299 A031300 A031301

Keyword

nonn,base,tabf,less,look

Author

Clark Kimberling

Extensions

Initial 0 and better name by Philippe Deléham, Oct 20 2011

Edited by M. F. Hasler, Jul 21 2013

Status

approved